CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS 被引量：1

CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

下载PDF

导出

摘要 We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient. For regular initial data, we show that the unique strong solution exits globally in time and converges to the equilibrium state time asymptotically. When initial density is piecewise regular with jump discontinuity, we show that there exists a unique global piecewise regular solution. In particular, the jump discontinuity of the density decays exponentially and the piecewise regular solution tends to the equilibrium state as t →＋∞ We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient. For regular initial data, we show that the unique strong solution exits globally in time and converges to the equilibrium state time asymptotically. When initial density is piecewise regular with jump discontinuity, we show that there exists a unique global piecewise regular solution. In particular, the jump discontinuity of the density decays exponentially and the piecewise regular solution tends to the equilibrium state as t →＋∞

作者连汝续刘健李海梁肖玲

机构地区 College of Mathematics and Information Science Department of Mathematics Academy of Mathematics and Systems Science

出处《Acta Mathematica Scientia》 SCIE CSCD 2012年第1期315-324,共10页 数学物理学报（B辑英文版）

基金 The research of R.X. Lian is supported by NSFC (11101145) The research of H.L. Li is partially supported by NSFC (10871134,11171228) the Huo Ying Dong Fund (111033) the Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHR201006107) The research of L. Xiao is supported by NSFC (11171327)

关键词 Navier-Stokes equations discontinuous initial data Navier-Stokes equations discontinuous initial data

分类号 O175.29 [理学—基础数学]

引文网络
相关文献

参考文献23

1Chen G, Hoff D, Trivisa K. Global solutions of the compressible Navier-Stokes equations with large dis- continuous initial data. Comm Partial Differ Equ, 2000, 25(11/12): 2233-2257.
2Fang D, Zhang T. Global solutions of the Navier-Stokes equations for compressible flow with density- dependent viscosity and discontinuous initial data. J Differ Equ, 2006, 222:63-94.
3Guo Z, Jiu Q, Xin Z. Spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients. SIAM J Math Anal, 2008, 39(5): 1402-1427.
4Hoff D. Constructin of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data. Proc Roy Soc Edinburgh Sect, 1986, A103:301-315.
5Hoff D. Global existence for 1D, compressible, isentropic Navier-Stokes equations with large initial data. Trans Amer Math Soc. 1987. 303(1): 169-181.
6Hoff D. Global well-posedness of the Cauchy problem for nonisentropic gas dynamics with discontinuous initial data. J Differ Equ, 1992, 95:33-73.
7Hoff D. Spherically symmetric solutions of the Navier-Stokes equations for compressible, isothermal flow with large, discontinuous initial data. Indiana Univ Math J, 1992, 41:1225-1302.
8Hoff D. Global solutions of the Navier-Stokes equations for multidimensonal compressible flow with dis- continuous initial data. J Differ Equ, 1995, 120:215-254.
9Hoff D. Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data. Arch Rational Mech Anal, 1995, 132: 1-14.
10Holt D, Discontinuous solutions of the Navier-Stokes equations for multidimensional flows of heat-conducting fluids. Arch Rational Mech Anal, 1997, 139(4): 303-354.